Highest Common Factor of 782, 497, 806 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 782, 497, 806 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 782, 497, 806 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 782, 497, 806 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 782, 497, 806 is 1.

HCF(782, 497, 806) = 1

HCF of 782, 497, 806 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 782, 497, 806 is 1.

Highest Common Factor of 782,497,806 using Euclid's algorithm

Highest Common Factor of 782,497,806 is 1

Step 1: Since 782 > 497, we apply the division lemma to 782 and 497, to get

782 = 497 x 1 + 285

Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 285 and 497, to get

497 = 285 x 1 + 212

Step 3: We consider the new divisor 285 and the new remainder 212, and apply the division lemma to get

285 = 212 x 1 + 73

We consider the new divisor 212 and the new remainder 73,and apply the division lemma to get

212 = 73 x 2 + 66

We consider the new divisor 73 and the new remainder 66,and apply the division lemma to get

73 = 66 x 1 + 7

We consider the new divisor 66 and the new remainder 7,and apply the division lemma to get

66 = 7 x 9 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 782 and 497 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(66,7) = HCF(73,66) = HCF(212,73) = HCF(285,212) = HCF(497,285) = HCF(782,497) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 806 > 1, we apply the division lemma to 806 and 1, to get

806 = 1 x 806 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 806 is 1

Notice that 1 = HCF(806,1) .

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Frequently Asked Questions on HCF of 782, 497, 806 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 782, 497, 806?

Answer: HCF of 782, 497, 806 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 782, 497, 806 using Euclid's Algorithm?

Answer: For arbitrary numbers 782, 497, 806 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.